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<div class="title">jama_eig.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef JAMA_EIG_H</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define JAMA_EIG_H</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;</div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#include &quot;tnt_array1d.h&quot;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#include &quot;tnt_array2d.h&quot;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="preprocessor">#include &quot;tnt_math_utils.h&quot;</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;</div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="preprocessor">#include &lt;algorithm&gt;</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">// for min(), max() below</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;</div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">// for abs() below</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;</div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">using namespace </span>TNT;</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">using namespace </span>std;</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="keyword">namespace </span>JAMA</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;{</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> Real&gt;</div>
<div class="line"><a name="l00072"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_eigenvalue.html">   72</a></span>&#160;<span class="keyword">class </span><a class="code" href="class_j_a_m_a_1_1_eigenvalue.html">Eigenvalue</a></div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;{</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <span class="keywordtype">int</span> n;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;   <span class="keywordtype">int</span> issymmetric; <span class="comment">/* boolean*/</span></div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;   <a class="code" href="class_t_n_t_1_1_array1_d.html">TNT::Array1D&lt;Real&gt;</a> d;         <span class="comment">/* real part */</span></div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;   <a class="code" href="class_t_n_t_1_1_array1_d.html">TNT::Array1D&lt;Real&gt;</a> e;         <span class="comment">/* img part */</span></div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    <a class="code" href="class_t_n_t_1_1_array2_d.html">TNT::Array2D&lt;Real&gt;</a> V;</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;   <a class="code" href="class_t_n_t_1_1_array2_d.html">TNT::Array2D&lt;Real&gt;</a> H;</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;   </div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;   <a class="code" href="class_t_n_t_1_1_array1_d.html">TNT::Array1D&lt;Real&gt;</a> ort;</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;   <span class="comment">// Symmetric Householder reduction to tridiagonal form.</span></div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;   <span class="keywordtype">void</span> tred2() {</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;   <span class="comment">//  This is derived from the Algol procedures tred2 by</span></div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;   <span class="comment">//  Bowdler, Martin, Reinsch, and Wilkinson, Handbook for</span></div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;   <span class="comment">//  Auto. Comp., Vol.ii-Linear Algebra, and the corresponding</span></div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;   <span class="comment">//  Fortran subroutine in EISPACK.</span></div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;         d[j] = V[n-1][j];</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;      }</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;      <span class="comment">// Householder reduction to tridiagonal form.</span></div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;   </div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n-1; i &gt; 0; i--) {</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;   </div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;         <span class="comment">// Scale to avoid under/overflow.</span></div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;   </div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;         Real scale = 0.0;</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;         Real h = 0.0;</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; i; k++) {</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;            scale = scale + abs(d[k]);</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;         }</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;         <span class="keywordflow">if</span> (scale == 0.0) {</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;            e[i] = d[i-1];</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; i; j++) {</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;               d[j] = V[i-1][j];</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;               V[i][j] = 0.0;</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;               V[j][i] = 0.0;</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;            }</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;         } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;   </div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;            <span class="comment">// Generate Householder vector.</span></div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;   </div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; i; k++) {</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;               d[k] /= scale;</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;               h += d[k] * d[k];</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;            }</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;            Real f = d[i-1];</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;            Real g = sqrt(h);</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;            <span class="keywordflow">if</span> (f &gt; 0) {</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;               g = -g;</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;            }</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;            e[i] = scale * g;</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;            h = h - f * g;</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;            d[i-1] = f - g;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; i; j++) {</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;               e[j] = 0.0;</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;            }</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;   </div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;            <span class="comment">// Apply similarity transformation to remaining columns.</span></div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;   </div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; i; j++) {</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;               f = d[j];</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;               V[j][i] = f;</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;               g = e[j] + V[j][j] * f;</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = j+1; k &lt;= i-1; k++) {</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;                  g += V[k][j] * d[k];</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;                  e[k] += V[k][j] * f;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;               }</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;               e[j] = g;</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;            }</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;            f = 0.0;</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; i; j++) {</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;               e[j] /= h;</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;               f += e[j] * d[j];</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;            }</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;            Real hh = f / (h + h);</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; i; j++) {</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;               e[j] -= hh * d[j];</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;            }</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; i; j++) {</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;               f = d[j];</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;               g = e[j];</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = j; k &lt;= i-1; k++) {</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;                  V[k][j] -= (f * e[k] + g * d[k]);</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;               }</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;               d[j] = V[i-1][j];</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;               V[i][j] = 0.0;</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;            }</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;         }</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;         d[i] = h;</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;      }</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;   </div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;      <span class="comment">// Accumulate transformations.</span></div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;   </div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n-1; i++) {</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;         V[n-1][i] = V[i][i];</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;         V[i][i] = 1.0;</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;         Real h = d[i+1];</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;         <span class="keywordflow">if</span> (h != 0.0) {</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt;= i; k++) {</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;               d[k] = V[k][i+1] / h;</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;            }</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt;= i; j++) {</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;               Real g = 0.0;</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt;= i; k++) {</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;                  g += V[k][i+1] * V[k][j];</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;               }</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt;= i; k++) {</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;                  V[k][j] -= g * d[k];</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;               }</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;            }</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;         }</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt;= i; k++) {</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;            V[k][i+1] = 0.0;</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;         }</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;      }</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;         d[j] = V[n-1][j];</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;         V[n-1][j] = 0.0;</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;      }</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;      V[n-1][n-1] = 1.0;</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;      e[0] = 0.0;</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;   } </div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;   <span class="comment">// Symmetric tridiagonal QL algorithm.</span></div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;   </div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;   <span class="keywordtype">void</span> tql2 () {</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;   <span class="comment">//  This is derived from the Algol procedures tql2, by</span></div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;   <span class="comment">//  Bowdler, Martin, Reinsch, and Wilkinson, Handbook for</span></div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;   <span class="comment">//  Auto. Comp., Vol.ii-Linear Algebra, and the corresponding</span></div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;   <span class="comment">//  Fortran subroutine in EISPACK.</span></div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;   </div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; n; i++) {</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;         e[i-1] = e[i];</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;      }</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;      e[n-1] = 0.0;</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;   </div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;      Real f = 0.0;</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;      Real tst1 = 0.0;</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;      Real eps = pow(2.0,-52.0);</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = 0; l &lt; n; l++) {</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;         <span class="comment">// Find small subdiagonal element</span></div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;   </div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;         tst1 = max(tst1,abs(d[l]) + abs(e[l]));</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;         <span class="keywordtype">int</span> m = l;</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;        <span class="comment">// Original while-loop from Java code</span></div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;         <span class="keywordflow">while</span> (m &lt; n) {</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;            <span class="keywordflow">if</span> (abs(e[m]) &lt;= eps*tst1) {</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;               <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;            }</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;            m++;</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;         }</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;   </div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;         <span class="comment">// If m == l, d[l] is an eigenvalue,</span></div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;         <span class="comment">// otherwise, iterate.</span></div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;   </div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;         <span class="keywordflow">if</span> (m &gt; l) {</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;            <span class="keywordtype">int</span> iter = 0;</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;            <span class="keywordflow">do</span> {</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;               iter = iter + 1;  <span class="comment">// (Could check iteration count here.)</span></div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;   </div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;               <span class="comment">// Compute implicit shift</span></div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;   </div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;               Real g = d[l];</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;               Real p = (d[l+1] - g) / (2.0 * e[l]);</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;               Real r = <a class="code" href="namespace_t_n_t.html#ae102d1c8992a4fea1cc1b2efeabfcc66">hypot</a>(p,1.0);</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;               <span class="keywordflow">if</span> (p &lt; 0) {</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;                  r = -r;</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;               }</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;               d[l] = e[l] / (p + r);</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;               d[l+1] = e[l] * (p + r);</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;               Real dl1 = d[l+1];</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;               Real h = g - d[l];</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = l+2; i &lt; n; i++) {</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;                  d[i] -= h;</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;               }</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;               f = f + h;</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;   </div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;               <span class="comment">// Implicit QL transformation.</span></div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;   </div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;               p = d[m];</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;               Real c = 1.0;</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;               Real c2 = c;</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;               Real c3 = c;</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;               Real el1 = e[l+1];</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;               Real s = 0.0;</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;               Real s2 = 0.0;</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = m-1; i &gt;= l; i--) {</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;                  c3 = c2;</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;                  c2 = c;</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;                  s2 = s;</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;                  g = c * e[i];</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;                  h = c * p;</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;                  r = <a class="code" href="namespace_t_n_t.html#ae102d1c8992a4fea1cc1b2efeabfcc66">hypot</a>(p,e[i]);</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;                  e[i+1] = s * r;</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;                  s = e[i] / r;</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;                  c = p / r;</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;                  p = c * d[i] - s * g;</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;                  d[i+1] = h + s * (c * g + s * d[i]);</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;   </div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;                  <span class="comment">// Accumulate transformation.</span></div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;   </div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;                  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; n; k++) {</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;                     h = V[k][i+1];</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;                     V[k][i+1] = s * V[k][i] + c * h;</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;                     V[k][i] = c * V[k][i] - s * h;</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;                  }</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;               }</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;               p = -s * s2 * c3 * el1 * e[l] / dl1;</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;               e[l] = s * p;</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;               d[l] = c * p;</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;   </div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;               <span class="comment">// Check for convergence.</span></div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;   </div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;            } <span class="keywordflow">while</span> (abs(e[l]) &gt; eps*tst1);</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;         }</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;         d[l] = d[l] + f;</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;         e[l] = 0.0;</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;      }</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;     </div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;      <span class="comment">// Sort eigenvalues and corresponding vectors.</span></div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;   </div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n-1; i++) {</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;         <span class="keywordtype">int</span> k = i;</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;         Real p = d[i];</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i+1; j &lt; n; j++) {</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;            <span class="keywordflow">if</span> (d[j] &lt; p) {</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;               k = j;</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;               p = d[j];</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;            }</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;         }</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;         <span class="keywordflow">if</span> (k != i) {</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;            d[k] = d[i];</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;            d[i] = p;</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;               p = V[j][i];</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;               V[j][i] = V[j][k];</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;               V[j][k] = p;</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;            }</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;         }</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;      }</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;   }</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;   <span class="comment">// Nonsymmetric reduction to Hessenberg form.</span></div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;   <span class="keywordtype">void</span> orthes () {</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;   </div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;      <span class="comment">//  This is derived from the Algol procedures orthes and ortran,</span></div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;      <span class="comment">//  by Martin and Wilkinson, Handbook for Auto. Comp.,</span></div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;      <span class="comment">//  Vol.ii-Linear Algebra, and the corresponding</span></div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;      <span class="comment">//  Fortran subroutines in EISPACK.</span></div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;   </div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;      <span class="keywordtype">int</span> low = 0;</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;      <span class="keywordtype">int</span> high = n-1;</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;   </div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> m = low+1; m &lt;= high-1; m++) {</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;   </div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;         <span class="comment">// Scale column.</span></div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;   </div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;         Real scale = 0.0;</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = m; i &lt;= high; i++) {</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;            scale = scale + abs(H[i][m-1]);</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;         }</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;         <span class="keywordflow">if</span> (scale != 0.0) {</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;   </div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;            <span class="comment">// Compute Householder transformation.</span></div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;   </div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;            Real h = 0.0;</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = high; i &gt;= m; i--) {</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;               ort[i] = H[i][m-1]/scale;</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;               h += ort[i] * ort[i];</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;            }</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;            Real g = sqrt(h);</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;            <span class="keywordflow">if</span> (ort[m] &gt; 0) {</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;               g = -g;</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;            }</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;            h = h - ort[m] * g;</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;            ort[m] = ort[m] - g;</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;   </div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;            <span class="comment">// Apply Householder similarity transformation</span></div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;            <span class="comment">// H = (I-u*u&#39;/h)*H*(I-u*u&#39;)/h)</span></div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;   </div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = m; j &lt; n; j++) {</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;               Real f = 0.0;</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = high; i &gt;= m; i--) {</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;                  f += ort[i]*H[i][j];</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;               }</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;               f = f/h;</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = m; i &lt;= high; i++) {</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;                  H[i][j] -= f*ort[i];</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;               }</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;           }</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;   </div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;           <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= high; i++) {</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;               Real f = 0.0;</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = high; j &gt;= m; j--) {</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;                  f += ort[j]*H[i][j];</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;               }</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;               f = f/h;</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = m; j &lt;= high; j++) {</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;                  H[i][j] -= f*ort[j];</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;               }</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;            }</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;            ort[m] = scale*ort[m];</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;            H[m][m-1] = scale*g;</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;         }</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;      }</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;   </div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;      <span class="comment">// Accumulate transformations (Algol&#39;s ortran).</span></div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;            V[i][j] = (i == j ? 1.0 : 0.0);</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;         }</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;      }</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> m = high-1; m &gt;= low+1; m--) {</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;         <span class="keywordflow">if</span> (H[m][m-1] != 0.0) {</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = m+1; i &lt;= high; i++) {</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;               ort[i] = H[i][m-1];</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;            }</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = m; j &lt;= high; j++) {</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;               Real g = 0.0;</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = m; i &lt;= high; i++) {</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;                  g += ort[i] * V[i][j];</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;               }</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;               <span class="comment">// Double division avoids possible underflow</span></div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;               g = (g / ort[m]) / H[m][m-1];</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = m; i &lt;= high; i++) {</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;                  V[i][j] += g * ort[i];</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;               }</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;            }</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;         }</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;      }</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;   }</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;   <span class="comment">// Complex scalar division.</span></div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;   Real cdivr, cdivi;</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;   <span class="keywordtype">void</span> cdiv(Real xr, Real xi, Real yr, Real yi) {</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;      Real r,d;</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;      <span class="keywordflow">if</span> (abs(yr) &gt; abs(yi)) {</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;         r = yi/yr;</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;         d = yr + r*yi;</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;         cdivr = (xr + r*xi)/d;</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;         cdivi = (xi - r*xr)/d;</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;      } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;         r = yr/yi;</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;         d = yi + r*yr;</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;         cdivr = (r*xr + xi)/d;</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;         cdivi = (r*xi - xr)/d;</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;      }</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;   }</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;   <span class="comment">// Nonsymmetric reduction from Hessenberg to real Schur form.</span></div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;   <span class="keywordtype">void</span> hqr2 () {</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;   </div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;      <span class="comment">//  This is derived from the Algol procedure hqr2,</span></div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;      <span class="comment">//  by Martin and Wilkinson, Handbook for Auto. Comp.,</span></div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;      <span class="comment">//  Vol.ii-Linear Algebra, and the corresponding</span></div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;      <span class="comment">//  Fortran subroutine in EISPACK.</span></div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;   </div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;      <span class="comment">// Initialize</span></div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;   </div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;      <span class="keywordtype">int</span> nn = this-&gt;n;</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;      <span class="keywordtype">int</span> n = nn-1;</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;      <span class="keywordtype">int</span> low = 0;</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;      <span class="keywordtype">int</span> high = nn-1;</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;      Real eps = pow(2.0,-52.0);</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;      Real exshift = 0.0;</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;      Real p=0,q=0,r=0,s=0,z=0,t,w,x,y;</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;   </div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;      <span class="comment">// Store roots isolated by balanc and compute matrix norm</span></div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;   </div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;      Real norm = 0.0;</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; nn; i++) {</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;         <span class="keywordflow">if</span> ((i &lt; low) || (i &gt; high)) {</div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;            d[i] = H[i][i];</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;            e[i] = 0.0;</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;         }</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = max(i-1,0); j &lt; nn; j++) {</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;            norm = norm + abs(H[i][j]);</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;         }</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;      }</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;   </div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;      <span class="comment">// Outer loop over eigenvalue index</span></div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;   </div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;      <span class="keywordtype">int</span> iter = 0;</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;      <span class="keywordflow">while</span> (n &gt;= low) {</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;   </div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;         <span class="comment">// Look for single small sub-diagonal element</span></div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;   </div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;         <span class="keywordtype">int</span> l = n;</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;         <span class="keywordflow">while</span> (l &gt; low) {</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;            s = abs(H[l-1][l-1]) + abs(H[l][l]);</div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;            <span class="keywordflow">if</span> (s == 0.0) {</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;               s = norm;</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;            }</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;            <span class="keywordflow">if</span> (abs(H[l][l-1]) &lt; eps * s) {</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;               <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;            }</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;            l--;</div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;         }</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;       </div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;         <span class="comment">// Check for convergence</span></div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;         <span class="comment">// One root found</span></div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;   </div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;         <span class="keywordflow">if</span> (l == n) {</div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;            H[n][n] = H[n][n] + exshift;</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;            d[n] = H[n][n];</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;            e[n] = 0.0;</div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;            n--;</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;            iter = 0;</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;   </div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;         <span class="comment">// Two roots found</span></div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;   </div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;         } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (l == n-1) {</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;            w = H[n][n-1] * H[n-1][n];</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;            p = (H[n-1][n-1] - H[n][n]) / 2.0;</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;            q = p * p + w;</div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;            z = sqrt(abs(q));</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;            H[n][n] = H[n][n] + exshift;</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;            H[n-1][n-1] = H[n-1][n-1] + exshift;</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;            x = H[n][n];</div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;   </div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;            <span class="comment">// Real pair</span></div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;   </div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;            <span class="keywordflow">if</span> (q &gt;= 0) {</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;               <span class="keywordflow">if</span> (p &gt;= 0) {</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;                  z = p + z;</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;               } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;                  z = p - z;</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;               }</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;               d[n-1] = x + z;</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;               d[n] = d[n-1];</div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;               <span class="keywordflow">if</span> (z != 0.0) {</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;                  d[n] = x - w / z;</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;               }</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;               e[n-1] = 0.0;</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;               e[n] = 0.0;</div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;               x = H[n][n-1];</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;               s = abs(x) + abs(z);</div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;               p = x / s;</div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;               q = z / s;</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;               r = sqrt(p * p+q * q);</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;               p = p / r;</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;               q = q / r;</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;   </div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;               <span class="comment">// Row modification</span></div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;   </div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = n-1; j &lt; nn; j++) {</div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;                  z = H[n-1][j];</div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;                  H[n-1][j] = q * z + p * H[n][j];</div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;                  H[n][j] = q * H[n][j] - p * z;</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;               }</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;   </div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;               <span class="comment">// Column modification</span></div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;   </div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= n; i++) {</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;                  z = H[i][n-1];</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;                  H[i][n-1] = q * z + p * H[i][n];</div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;                  H[i][n] = q * H[i][n] - p * z;</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;               }</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;   </div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;               <span class="comment">// Accumulate transformations</span></div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;   </div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = low; i &lt;= high; i++) {</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;                  z = V[i][n-1];</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;                  V[i][n-1] = q * z + p * V[i][n];</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;                  V[i][n] = q * V[i][n] - p * z;</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;               }</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;   </div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;            <span class="comment">// Complex pair</span></div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;   </div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;            } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;               d[n-1] = x + p;</div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;               d[n] = x + p;</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;               e[n-1] = z;</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;               e[n] = -z;</div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;            }</div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;            n = n - 2;</div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;            iter = 0;</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;   </div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;         <span class="comment">// No convergence yet</span></div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;   </div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;         } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;   </div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;            <span class="comment">// Form shift</span></div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;   </div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;            x = H[n][n];</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;            y = 0.0;</div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;            w = 0.0;</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;            <span class="keywordflow">if</span> (l &lt; n) {</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;               y = H[n-1][n-1];</div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;               w = H[n][n-1] * H[n-1][n];</div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;            }</div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;   </div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;            <span class="comment">// Wilkinson&#39;s original ad hoc shift</span></div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;   </div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;            <span class="keywordflow">if</span> (iter == 10) {</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;               exshift += x;</div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = low; i &lt;= n; i++) {</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;                  H[i][i] -= x;</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;               }</div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;               s = abs(H[n][n-1]) + abs(H[n-1][n-2]);</div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;               x = y = 0.75 * s;</div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;               w = -0.4375 * s * s;</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;            }</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160;</div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;            <span class="comment">// MATLAB&#39;s new ad hoc shift</span></div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;            <span class="keywordflow">if</span> (iter == 30) {</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;                s = (y - x) / 2.0;</div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160;                s = s * s + w;</div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;                <span class="keywordflow">if</span> (s &gt; 0) {</div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;                    s = sqrt(s);</div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;                    <span class="keywordflow">if</span> (y &lt; x) {</div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;                       s = -s;</div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;                    }</div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;                    s = x - w / ((y - x) / 2.0 + s);</div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;                    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = low; i &lt;= n; i++) {</div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160;                       H[i][i] -= s;</div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160;                    }</div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;                    exshift += s;</div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;                    x = y = w = 0.964;</div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;                }</div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;            }</div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;   </div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;            iter = iter + 1;   <span class="comment">// (Could check iteration count here.)</span></div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;   </div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;            <span class="comment">// Look for two consecutive small sub-diagonal elements</span></div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160;   </div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160;            <span class="keywordtype">int</span> m = n-2;</div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160;            <span class="keywordflow">while</span> (m &gt;= l) {</div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160;               z = H[m][m];</div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160;               r = x - z;</div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;               s = y - z;</div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160;               p = (r * s - w) / H[m+1][m] + H[m][m+1];</div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;               q = H[m+1][m+1] - z - r - s;</div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160;               r = H[m+2][m+1];</div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160;               s = abs(p) + abs(q) + abs(r);</div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;               p = p / s;</div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;               q = q / s;</div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160;               r = r / s;</div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160;               <span class="keywordflow">if</span> (m == l) {</div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;                  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;               }</div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;               <span class="keywordflow">if</span> (abs(H[m][m-1]) * (abs(q) + abs(r)) &lt;</div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160;                  eps * (abs(p) * (abs(H[m-1][m-1]) + abs(z) +</div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;                  abs(H[m+1][m+1])))) {</div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160;                     <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160;               }</div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160;               m--;</div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160;            }</div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;   </div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = m+2; i &lt;= n; i++) {</div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160;               H[i][i-2] = 0.0;</div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;               <span class="keywordflow">if</span> (i &gt; m+2) {</div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160;                  H[i][i-3] = 0.0;</div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160;               }</div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160;            }</div>
<div class="line"><a name="l00662"></a><span class="lineno">  662</span>&#160;   </div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;            <span class="comment">// Double QR step involving rows l:n and columns m:n</span></div>
<div class="line"><a name="l00664"></a><span class="lineno">  664</span>&#160;   </div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = m; k &lt;= n-1; k++) {</div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;               <span class="keywordtype">int</span> notlast = (k != n-1);</div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160;               <span class="keywordflow">if</span> (k != m) {</div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160;                  p = H[k][k-1];</div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;                  q = H[k+1][k-1];</div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160;                  r = (notlast ? H[k+2][k-1] : 0.0);</div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160;                  x = abs(p) + abs(q) + abs(r);</div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160;                  <span class="keywordflow">if</span> (x != 0.0) {</div>
<div class="line"><a name="l00673"></a><span class="lineno">  673</span>&#160;                     p = p / x;</div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160;                     q = q / x;</div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160;                     r = r / x;</div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160;                  }</div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;               }</div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;               <span class="keywordflow">if</span> (x == 0.0) {</div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;                  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160;               }</div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160;               s = sqrt(p * p + q * q + r * r);</div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160;               <span class="keywordflow">if</span> (p &lt; 0) {</div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;                  s = -s;</div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160;               }</div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160;               <span class="keywordflow">if</span> (s != 0) {</div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160;                  <span class="keywordflow">if</span> (k != m) {</div>
<div class="line"><a name="l00687"></a><span class="lineno">  687</span>&#160;                     H[k][k-1] = -s * x;</div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160;                  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (l != m) {</div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160;                     H[k][k-1] = -H[k][k-1];</div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160;                  }</div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160;                  p = p + s;</div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160;                  x = p / s;</div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160;                  y = q / s;</div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160;                  z = r / s;</div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160;                  q = q / p;</div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160;                  r = r / p;</div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;   </div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160;                  <span class="comment">// Row modification</span></div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160;   </div>
<div class="line"><a name="l00700"></a><span class="lineno">  700</span>&#160;                  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = k; j &lt; nn; j++) {</div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160;                     p = H[k][j] + q * H[k+1][j];</div>
<div class="line"><a name="l00702"></a><span class="lineno">  702</span>&#160;                     <span class="keywordflow">if</span> (notlast) {</div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160;                        p = p + r * H[k+2][j];</div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160;                        H[k+2][j] = H[k+2][j] - p * z;</div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;                     }</div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160;                     H[k][j] = H[k][j] - p * x;</div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160;                     H[k+1][j] = H[k+1][j] - p * y;</div>
<div class="line"><a name="l00708"></a><span class="lineno">  708</span>&#160;                  }</div>
<div class="line"><a name="l00709"></a><span class="lineno">  709</span>&#160;   </div>
<div class="line"><a name="l00710"></a><span class="lineno">  710</span>&#160;                  <span class="comment">// Column modification</span></div>
<div class="line"><a name="l00711"></a><span class="lineno">  711</span>&#160;   </div>
<div class="line"><a name="l00712"></a><span class="lineno">  712</span>&#160;                  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= min(n,k+3); i++) {</div>
<div class="line"><a name="l00713"></a><span class="lineno">  713</span>&#160;                     p = x * H[i][k] + y * H[i][k+1];</div>
<div class="line"><a name="l00714"></a><span class="lineno">  714</span>&#160;                     <span class="keywordflow">if</span> (notlast) {</div>
<div class="line"><a name="l00715"></a><span class="lineno">  715</span>&#160;                        p = p + z * H[i][k+2];</div>
<div class="line"><a name="l00716"></a><span class="lineno">  716</span>&#160;                        H[i][k+2] = H[i][k+2] - p * r;</div>
<div class="line"><a name="l00717"></a><span class="lineno">  717</span>&#160;                     }</div>
<div class="line"><a name="l00718"></a><span class="lineno">  718</span>&#160;                     H[i][k] = H[i][k] - p;</div>
<div class="line"><a name="l00719"></a><span class="lineno">  719</span>&#160;                     H[i][k+1] = H[i][k+1] - p * q;</div>
<div class="line"><a name="l00720"></a><span class="lineno">  720</span>&#160;                  }</div>
<div class="line"><a name="l00721"></a><span class="lineno">  721</span>&#160;   </div>
<div class="line"><a name="l00722"></a><span class="lineno">  722</span>&#160;                  <span class="comment">// Accumulate transformations</span></div>
<div class="line"><a name="l00723"></a><span class="lineno">  723</span>&#160;   </div>
<div class="line"><a name="l00724"></a><span class="lineno">  724</span>&#160;                  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = low; i &lt;= high; i++) {</div>
<div class="line"><a name="l00725"></a><span class="lineno">  725</span>&#160;                     p = x * V[i][k] + y * V[i][k+1];</div>
<div class="line"><a name="l00726"></a><span class="lineno">  726</span>&#160;                     <span class="keywordflow">if</span> (notlast) {</div>
<div class="line"><a name="l00727"></a><span class="lineno">  727</span>&#160;                        p = p + z * V[i][k+2];</div>
<div class="line"><a name="l00728"></a><span class="lineno">  728</span>&#160;                        V[i][k+2] = V[i][k+2] - p * r;</div>
<div class="line"><a name="l00729"></a><span class="lineno">  729</span>&#160;                     }</div>
<div class="line"><a name="l00730"></a><span class="lineno">  730</span>&#160;                     V[i][k] = V[i][k] - p;</div>
<div class="line"><a name="l00731"></a><span class="lineno">  731</span>&#160;                     V[i][k+1] = V[i][k+1] - p * q;</div>
<div class="line"><a name="l00732"></a><span class="lineno">  732</span>&#160;                  }</div>
<div class="line"><a name="l00733"></a><span class="lineno">  733</span>&#160;               }  <span class="comment">// (s != 0)</span></div>
<div class="line"><a name="l00734"></a><span class="lineno">  734</span>&#160;            }  <span class="comment">// k loop</span></div>
<div class="line"><a name="l00735"></a><span class="lineno">  735</span>&#160;         }  <span class="comment">// check convergence</span></div>
<div class="line"><a name="l00736"></a><span class="lineno">  736</span>&#160;      }  <span class="comment">// while (n &gt;= low)</span></div>
<div class="line"><a name="l00737"></a><span class="lineno">  737</span>&#160;      </div>
<div class="line"><a name="l00738"></a><span class="lineno">  738</span>&#160;      <span class="comment">// Backsubstitute to find vectors of upper triangular form</span></div>
<div class="line"><a name="l00739"></a><span class="lineno">  739</span>&#160;</div>
<div class="line"><a name="l00740"></a><span class="lineno">  740</span>&#160;      <span class="keywordflow">if</span> (norm == 0.0) {</div>
<div class="line"><a name="l00741"></a><span class="lineno">  741</span>&#160;         <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00742"></a><span class="lineno">  742</span>&#160;      }</div>
<div class="line"><a name="l00743"></a><span class="lineno">  743</span>&#160;   </div>
<div class="line"><a name="l00744"></a><span class="lineno">  744</span>&#160;      <span class="keywordflow">for</span> (n = nn-1; n &gt;= 0; n--) {</div>
<div class="line"><a name="l00745"></a><span class="lineno">  745</span>&#160;         p = d[n];</div>
<div class="line"><a name="l00746"></a><span class="lineno">  746</span>&#160;         q = e[n];</div>
<div class="line"><a name="l00747"></a><span class="lineno">  747</span>&#160;   </div>
<div class="line"><a name="l00748"></a><span class="lineno">  748</span>&#160;         <span class="comment">// Real vector</span></div>
<div class="line"><a name="l00749"></a><span class="lineno">  749</span>&#160;   </div>
<div class="line"><a name="l00750"></a><span class="lineno">  750</span>&#160;         <span class="keywordflow">if</span> (q == 0) {</div>
<div class="line"><a name="l00751"></a><span class="lineno">  751</span>&#160;            <span class="keywordtype">int</span> l = n;</div>
<div class="line"><a name="l00752"></a><span class="lineno">  752</span>&#160;            H[n][n] = 1.0;</div>
<div class="line"><a name="l00753"></a><span class="lineno">  753</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n-1; i &gt;= 0; i--) {</div>
<div class="line"><a name="l00754"></a><span class="lineno">  754</span>&#160;               w = H[i][i] - p;</div>
<div class="line"><a name="l00755"></a><span class="lineno">  755</span>&#160;               r = 0.0;</div>
<div class="line"><a name="l00756"></a><span class="lineno">  756</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = l; j &lt;= n; j++) {</div>
<div class="line"><a name="l00757"></a><span class="lineno">  757</span>&#160;                  r = r + H[i][j] * H[j][n];</div>
<div class="line"><a name="l00758"></a><span class="lineno">  758</span>&#160;               }</div>
<div class="line"><a name="l00759"></a><span class="lineno">  759</span>&#160;               <span class="keywordflow">if</span> (e[i] &lt; 0.0) {</div>
<div class="line"><a name="l00760"></a><span class="lineno">  760</span>&#160;                  z = w;</div>
<div class="line"><a name="l00761"></a><span class="lineno">  761</span>&#160;                  s = r;</div>
<div class="line"><a name="l00762"></a><span class="lineno">  762</span>&#160;               } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00763"></a><span class="lineno">  763</span>&#160;                  l = i;</div>
<div class="line"><a name="l00764"></a><span class="lineno">  764</span>&#160;                  <span class="keywordflow">if</span> (e[i] == 0.0) {</div>
<div class="line"><a name="l00765"></a><span class="lineno">  765</span>&#160;                     <span class="keywordflow">if</span> (w != 0.0) {</div>
<div class="line"><a name="l00766"></a><span class="lineno">  766</span>&#160;                        H[i][n] = -r / w;</div>
<div class="line"><a name="l00767"></a><span class="lineno">  767</span>&#160;                     } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00768"></a><span class="lineno">  768</span>&#160;                        H[i][n] = -r / (eps * norm);</div>
<div class="line"><a name="l00769"></a><span class="lineno">  769</span>&#160;                     }</div>
<div class="line"><a name="l00770"></a><span class="lineno">  770</span>&#160;   </div>
<div class="line"><a name="l00771"></a><span class="lineno">  771</span>&#160;                  <span class="comment">// Solve real equations</span></div>
<div class="line"><a name="l00772"></a><span class="lineno">  772</span>&#160;   </div>
<div class="line"><a name="l00773"></a><span class="lineno">  773</span>&#160;                  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00774"></a><span class="lineno">  774</span>&#160;                     x = H[i][i+1];</div>
<div class="line"><a name="l00775"></a><span class="lineno">  775</span>&#160;                     y = H[i+1][i];</div>
<div class="line"><a name="l00776"></a><span class="lineno">  776</span>&#160;                     q = (d[i] - p) * (d[i] - p) + e[i] * e[i];</div>
<div class="line"><a name="l00777"></a><span class="lineno">  777</span>&#160;                     t = (x * s - z * r) / q;</div>
<div class="line"><a name="l00778"></a><span class="lineno">  778</span>&#160;                     H[i][n] = t;</div>
<div class="line"><a name="l00779"></a><span class="lineno">  779</span>&#160;                     <span class="keywordflow">if</span> (abs(x) &gt; abs(z)) {</div>
<div class="line"><a name="l00780"></a><span class="lineno">  780</span>&#160;                        H[i+1][n] = (-r - w * t) / x;</div>
<div class="line"><a name="l00781"></a><span class="lineno">  781</span>&#160;                     } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00782"></a><span class="lineno">  782</span>&#160;                        H[i+1][n] = (-s - y * t) / z;</div>
<div class="line"><a name="l00783"></a><span class="lineno">  783</span>&#160;                     }</div>
<div class="line"><a name="l00784"></a><span class="lineno">  784</span>&#160;                  }</div>
<div class="line"><a name="l00785"></a><span class="lineno">  785</span>&#160;   </div>
<div class="line"><a name="l00786"></a><span class="lineno">  786</span>&#160;                  <span class="comment">// Overflow control</span></div>
<div class="line"><a name="l00787"></a><span class="lineno">  787</span>&#160;   </div>
<div class="line"><a name="l00788"></a><span class="lineno">  788</span>&#160;                  t = abs(H[i][n]);</div>
<div class="line"><a name="l00789"></a><span class="lineno">  789</span>&#160;                  <span class="keywordflow">if</span> ((eps * t) * t &gt; 1) {</div>
<div class="line"><a name="l00790"></a><span class="lineno">  790</span>&#160;                     <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i; j &lt;= n; j++) {</div>
<div class="line"><a name="l00791"></a><span class="lineno">  791</span>&#160;                        H[j][n] = H[j][n] / t;</div>
<div class="line"><a name="l00792"></a><span class="lineno">  792</span>&#160;                     }</div>
<div class="line"><a name="l00793"></a><span class="lineno">  793</span>&#160;                  }</div>
<div class="line"><a name="l00794"></a><span class="lineno">  794</span>&#160;               }</div>
<div class="line"><a name="l00795"></a><span class="lineno">  795</span>&#160;            }</div>
<div class="line"><a name="l00796"></a><span class="lineno">  796</span>&#160;   </div>
<div class="line"><a name="l00797"></a><span class="lineno">  797</span>&#160;         <span class="comment">// Complex vector</span></div>
<div class="line"><a name="l00798"></a><span class="lineno">  798</span>&#160;   </div>
<div class="line"><a name="l00799"></a><span class="lineno">  799</span>&#160;         } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (q &lt; 0) {</div>
<div class="line"><a name="l00800"></a><span class="lineno">  800</span>&#160;            <span class="keywordtype">int</span> l = n-1;</div>
<div class="line"><a name="l00801"></a><span class="lineno">  801</span>&#160;</div>
<div class="line"><a name="l00802"></a><span class="lineno">  802</span>&#160;            <span class="comment">// Last vector component imaginary so matrix is triangular</span></div>
<div class="line"><a name="l00803"></a><span class="lineno">  803</span>&#160;   </div>
<div class="line"><a name="l00804"></a><span class="lineno">  804</span>&#160;            <span class="keywordflow">if</span> (abs(H[n][n-1]) &gt; abs(H[n-1][n])) {</div>
<div class="line"><a name="l00805"></a><span class="lineno">  805</span>&#160;               H[n-1][n-1] = q / H[n][n-1];</div>
<div class="line"><a name="l00806"></a><span class="lineno">  806</span>&#160;               H[n-1][n] = -(H[n][n] - p) / H[n][n-1];</div>
<div class="line"><a name="l00807"></a><span class="lineno">  807</span>&#160;            } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00808"></a><span class="lineno">  808</span>&#160;               cdiv(0.0,-H[n-1][n],H[n-1][n-1]-p,q);</div>
<div class="line"><a name="l00809"></a><span class="lineno">  809</span>&#160;               H[n-1][n-1] = cdivr;</div>
<div class="line"><a name="l00810"></a><span class="lineno">  810</span>&#160;               H[n-1][n] = cdivi;</div>
<div class="line"><a name="l00811"></a><span class="lineno">  811</span>&#160;            }</div>
<div class="line"><a name="l00812"></a><span class="lineno">  812</span>&#160;            H[n][n-1] = 0.0;</div>
<div class="line"><a name="l00813"></a><span class="lineno">  813</span>&#160;            H[n][n] = 1.0;</div>
<div class="line"><a name="l00814"></a><span class="lineno">  814</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n-2; i &gt;= 0; i--) {</div>
<div class="line"><a name="l00815"></a><span class="lineno">  815</span>&#160;               Real ra,sa,vr,vi;</div>
<div class="line"><a name="l00816"></a><span class="lineno">  816</span>&#160;               ra = 0.0;</div>
<div class="line"><a name="l00817"></a><span class="lineno">  817</span>&#160;               sa = 0.0;</div>
<div class="line"><a name="l00818"></a><span class="lineno">  818</span>&#160;               <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = l; j &lt;= n; j++) {</div>
<div class="line"><a name="l00819"></a><span class="lineno">  819</span>&#160;                  ra = ra + H[i][j] * H[j][n-1];</div>
<div class="line"><a name="l00820"></a><span class="lineno">  820</span>&#160;                  sa = sa + H[i][j] * H[j][n];</div>
<div class="line"><a name="l00821"></a><span class="lineno">  821</span>&#160;               }</div>
<div class="line"><a name="l00822"></a><span class="lineno">  822</span>&#160;               w = H[i][i] - p;</div>
<div class="line"><a name="l00823"></a><span class="lineno">  823</span>&#160;   </div>
<div class="line"><a name="l00824"></a><span class="lineno">  824</span>&#160;               <span class="keywordflow">if</span> (e[i] &lt; 0.0) {</div>
<div class="line"><a name="l00825"></a><span class="lineno">  825</span>&#160;                  z = w;</div>
<div class="line"><a name="l00826"></a><span class="lineno">  826</span>&#160;                  r = ra;</div>
<div class="line"><a name="l00827"></a><span class="lineno">  827</span>&#160;                  s = sa;</div>
<div class="line"><a name="l00828"></a><span class="lineno">  828</span>&#160;               } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00829"></a><span class="lineno">  829</span>&#160;                  l = i;</div>
<div class="line"><a name="l00830"></a><span class="lineno">  830</span>&#160;                  <span class="keywordflow">if</span> (e[i] == 0) {</div>
<div class="line"><a name="l00831"></a><span class="lineno">  831</span>&#160;                     cdiv(-ra,-sa,w,q);</div>
<div class="line"><a name="l00832"></a><span class="lineno">  832</span>&#160;                     H[i][n-1] = cdivr;</div>
<div class="line"><a name="l00833"></a><span class="lineno">  833</span>&#160;                     H[i][n] = cdivi;</div>
<div class="line"><a name="l00834"></a><span class="lineno">  834</span>&#160;                  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00835"></a><span class="lineno">  835</span>&#160;   </div>
<div class="line"><a name="l00836"></a><span class="lineno">  836</span>&#160;                     <span class="comment">// Solve complex equations</span></div>
<div class="line"><a name="l00837"></a><span class="lineno">  837</span>&#160;   </div>
<div class="line"><a name="l00838"></a><span class="lineno">  838</span>&#160;                     x = H[i][i+1];</div>
<div class="line"><a name="l00839"></a><span class="lineno">  839</span>&#160;                     y = H[i+1][i];</div>
<div class="line"><a name="l00840"></a><span class="lineno">  840</span>&#160;                     vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;</div>
<div class="line"><a name="l00841"></a><span class="lineno">  841</span>&#160;                     vi = (d[i] - p) * 2.0 * q;</div>
<div class="line"><a name="l00842"></a><span class="lineno">  842</span>&#160;                     <span class="keywordflow">if</span> ((vr == 0.0) &amp;&amp; (vi == 0.0)) {</div>
<div class="line"><a name="l00843"></a><span class="lineno">  843</span>&#160;                        vr = eps * norm * (abs(w) + abs(q) +</div>
<div class="line"><a name="l00844"></a><span class="lineno">  844</span>&#160;                        abs(x) + abs(y) + abs(z));</div>
<div class="line"><a name="l00845"></a><span class="lineno">  845</span>&#160;                     }</div>
<div class="line"><a name="l00846"></a><span class="lineno">  846</span>&#160;                     cdiv(x*r-z*ra+q*sa,x*s-z*sa-q*ra,vr,vi);</div>
<div class="line"><a name="l00847"></a><span class="lineno">  847</span>&#160;                     H[i][n-1] = cdivr;</div>
<div class="line"><a name="l00848"></a><span class="lineno">  848</span>&#160;                     H[i][n] = cdivi;</div>
<div class="line"><a name="l00849"></a><span class="lineno">  849</span>&#160;                     <span class="keywordflow">if</span> (abs(x) &gt; (abs(z) + abs(q))) {</div>
<div class="line"><a name="l00850"></a><span class="lineno">  850</span>&#160;                        H[i+1][n-1] = (-ra - w * H[i][n-1] + q * H[i][n]) / x;</div>
<div class="line"><a name="l00851"></a><span class="lineno">  851</span>&#160;                        H[i+1][n] = (-sa - w * H[i][n] - q * H[i][n-1]) / x;</div>
<div class="line"><a name="l00852"></a><span class="lineno">  852</span>&#160;                     } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00853"></a><span class="lineno">  853</span>&#160;                        cdiv(-r-y*H[i][n-1],-s-y*H[i][n],z,q);</div>
<div class="line"><a name="l00854"></a><span class="lineno">  854</span>&#160;                        H[i+1][n-1] = cdivr;</div>
<div class="line"><a name="l00855"></a><span class="lineno">  855</span>&#160;                        H[i+1][n] = cdivi;</div>
<div class="line"><a name="l00856"></a><span class="lineno">  856</span>&#160;                     }</div>
<div class="line"><a name="l00857"></a><span class="lineno">  857</span>&#160;                  }</div>
<div class="line"><a name="l00858"></a><span class="lineno">  858</span>&#160;   </div>
<div class="line"><a name="l00859"></a><span class="lineno">  859</span>&#160;                  <span class="comment">// Overflow control</span></div>
<div class="line"><a name="l00860"></a><span class="lineno">  860</span>&#160;</div>
<div class="line"><a name="l00861"></a><span class="lineno">  861</span>&#160;                  t = max(abs(H[i][n-1]),abs(H[i][n]));</div>
<div class="line"><a name="l00862"></a><span class="lineno">  862</span>&#160;                  <span class="keywordflow">if</span> ((eps * t) * t &gt; 1) {</div>
<div class="line"><a name="l00863"></a><span class="lineno">  863</span>&#160;                     <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i; j &lt;= n; j++) {</div>
<div class="line"><a name="l00864"></a><span class="lineno">  864</span>&#160;                        H[j][n-1] = H[j][n-1] / t;</div>
<div class="line"><a name="l00865"></a><span class="lineno">  865</span>&#160;                        H[j][n] = H[j][n] / t;</div>
<div class="line"><a name="l00866"></a><span class="lineno">  866</span>&#160;                     }</div>
<div class="line"><a name="l00867"></a><span class="lineno">  867</span>&#160;                  }</div>
<div class="line"><a name="l00868"></a><span class="lineno">  868</span>&#160;               }</div>
<div class="line"><a name="l00869"></a><span class="lineno">  869</span>&#160;            }</div>
<div class="line"><a name="l00870"></a><span class="lineno">  870</span>&#160;         }</div>
<div class="line"><a name="l00871"></a><span class="lineno">  871</span>&#160;      }</div>
<div class="line"><a name="l00872"></a><span class="lineno">  872</span>&#160;   </div>
<div class="line"><a name="l00873"></a><span class="lineno">  873</span>&#160;      <span class="comment">// Vectors of isolated roots</span></div>
<div class="line"><a name="l00874"></a><span class="lineno">  874</span>&#160;   </div>
<div class="line"><a name="l00875"></a><span class="lineno">  875</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; nn; i++) {</div>
<div class="line"><a name="l00876"></a><span class="lineno">  876</span>&#160;         <span class="keywordflow">if</span> (i &lt; low || i &gt; high) {</div>
<div class="line"><a name="l00877"></a><span class="lineno">  877</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i; j &lt; nn; j++) {</div>
<div class="line"><a name="l00878"></a><span class="lineno">  878</span>&#160;               V[i][j] = H[i][j];</div>
<div class="line"><a name="l00879"></a><span class="lineno">  879</span>&#160;            }</div>
<div class="line"><a name="l00880"></a><span class="lineno">  880</span>&#160;         }</div>
<div class="line"><a name="l00881"></a><span class="lineno">  881</span>&#160;      }</div>
<div class="line"><a name="l00882"></a><span class="lineno">  882</span>&#160;   </div>
<div class="line"><a name="l00883"></a><span class="lineno">  883</span>&#160;      <span class="comment">// Back transformation to get eigenvectors of original matrix</span></div>
<div class="line"><a name="l00884"></a><span class="lineno">  884</span>&#160;   </div>
<div class="line"><a name="l00885"></a><span class="lineno">  885</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = nn-1; j &gt;= low; j--) {</div>
<div class="line"><a name="l00886"></a><span class="lineno">  886</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = low; i &lt;= high; i++) {</div>
<div class="line"><a name="l00887"></a><span class="lineno">  887</span>&#160;            z = 0.0;</div>
<div class="line"><a name="l00888"></a><span class="lineno">  888</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = low; k &lt;= min(j,high); k++) {</div>
<div class="line"><a name="l00889"></a><span class="lineno">  889</span>&#160;               z = z + V[i][k] * H[k][j];</div>
<div class="line"><a name="l00890"></a><span class="lineno">  890</span>&#160;            }</div>
<div class="line"><a name="l00891"></a><span class="lineno">  891</span>&#160;            V[i][j] = z;</div>
<div class="line"><a name="l00892"></a><span class="lineno">  892</span>&#160;         }</div>
<div class="line"><a name="l00893"></a><span class="lineno">  893</span>&#160;      }</div>
<div class="line"><a name="l00894"></a><span class="lineno">  894</span>&#160;   }</div>
<div class="line"><a name="l00895"></a><span class="lineno">  895</span>&#160;</div>
<div class="line"><a name="l00896"></a><span class="lineno">  896</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00897"></a><span class="lineno">  897</span>&#160;</div>
<div class="line"><a name="l00898"></a><span class="lineno">  898</span>&#160;</div>
<div class="line"><a name="l00903"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_eigenvalue.html#a28bf3e2df18bcd3d3f3b0979630953b3">  903</a></span>&#160;   <a class="code" href="class_j_a_m_a_1_1_eigenvalue.html#a28bf3e2df18bcd3d3f3b0979630953b3">Eigenvalue</a>(<span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array2_d.html">TNT::Array2D&lt;Real&gt;</a> &amp;A) {</div>
<div class="line"><a name="l00904"></a><span class="lineno">  904</span>&#160;      n = A.<a class="code" href="class_t_n_t_1_1_array2_d.html#a6efd5ac98f02bb42340be1d5cbf4c9c1">dim2</a>();</div>
<div class="line"><a name="l00905"></a><span class="lineno">  905</span>&#160;      V = <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a>(n,n);</div>
<div class="line"><a name="l00906"></a><span class="lineno">  906</span>&#160;      d = <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a>(n);</div>
<div class="line"><a name="l00907"></a><span class="lineno">  907</span>&#160;      e = <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a>(n);</div>
<div class="line"><a name="l00908"></a><span class="lineno">  908</span>&#160;</div>
<div class="line"><a name="l00909"></a><span class="lineno">  909</span>&#160;      issymmetric = 1;</div>
<div class="line"><a name="l00910"></a><span class="lineno">  910</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; (j &lt; n) &amp;&amp; issymmetric; j++) {</div>
<div class="line"><a name="l00911"></a><span class="lineno">  911</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; (i &lt; n) &amp;&amp; issymmetric; i++) {</div>
<div class="line"><a name="l00912"></a><span class="lineno">  912</span>&#160;            issymmetric = (A[i][j] == A[j][i]);</div>
<div class="line"><a name="l00913"></a><span class="lineno">  913</span>&#160;         }</div>
<div class="line"><a name="l00914"></a><span class="lineno">  914</span>&#160;      }</div>
<div class="line"><a name="l00915"></a><span class="lineno">  915</span>&#160;</div>
<div class="line"><a name="l00916"></a><span class="lineno">  916</span>&#160;      <span class="keywordflow">if</span> (issymmetric) {</div>
<div class="line"><a name="l00917"></a><span class="lineno">  917</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00918"></a><span class="lineno">  918</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a name="l00919"></a><span class="lineno">  919</span>&#160;               V[i][j] = A[i][j];</div>
<div class="line"><a name="l00920"></a><span class="lineno">  920</span>&#160;            }</div>
<div class="line"><a name="l00921"></a><span class="lineno">  921</span>&#160;         }</div>
<div class="line"><a name="l00922"></a><span class="lineno">  922</span>&#160;   </div>
<div class="line"><a name="l00923"></a><span class="lineno">  923</span>&#160;         <span class="comment">// Tridiagonalize.</span></div>
<div class="line"><a name="l00924"></a><span class="lineno">  924</span>&#160;         tred2();</div>
<div class="line"><a name="l00925"></a><span class="lineno">  925</span>&#160;   </div>
<div class="line"><a name="l00926"></a><span class="lineno">  926</span>&#160;         <span class="comment">// Diagonalize.</span></div>
<div class="line"><a name="l00927"></a><span class="lineno">  927</span>&#160;         tql2();</div>
<div class="line"><a name="l00928"></a><span class="lineno">  928</span>&#160;</div>
<div class="line"><a name="l00929"></a><span class="lineno">  929</span>&#160;      } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00930"></a><span class="lineno">  930</span>&#160;         H = <a class="code" href="class_t_n_t_1_1_array2_d.html">TNT::Array2D&lt;Real&gt;</a>(n,n);</div>
<div class="line"><a name="l00931"></a><span class="lineno">  931</span>&#160;         ort = <a class="code" href="class_t_n_t_1_1_array1_d.html">TNT::Array1D&lt;Real&gt;</a>(n);</div>
<div class="line"><a name="l00932"></a><span class="lineno">  932</span>&#160;         </div>
<div class="line"><a name="l00933"></a><span class="lineno">  933</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a name="l00934"></a><span class="lineno">  934</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00935"></a><span class="lineno">  935</span>&#160;               H[i][j] = A[i][j];</div>
<div class="line"><a name="l00936"></a><span class="lineno">  936</span>&#160;            }</div>
<div class="line"><a name="l00937"></a><span class="lineno">  937</span>&#160;         }</div>
<div class="line"><a name="l00938"></a><span class="lineno">  938</span>&#160;   </div>
<div class="line"><a name="l00939"></a><span class="lineno">  939</span>&#160;         <span class="comment">// Reduce to Hessenberg form.</span></div>
<div class="line"><a name="l00940"></a><span class="lineno">  940</span>&#160;         orthes();</div>
<div class="line"><a name="l00941"></a><span class="lineno">  941</span>&#160;   </div>
<div class="line"><a name="l00942"></a><span class="lineno">  942</span>&#160;         <span class="comment">// Reduce Hessenberg to real Schur form.</span></div>
<div class="line"><a name="l00943"></a><span class="lineno">  943</span>&#160;         hqr2();</div>
<div class="line"><a name="l00944"></a><span class="lineno">  944</span>&#160;      }</div>
<div class="line"><a name="l00945"></a><span class="lineno">  945</span>&#160;   }</div>
<div class="line"><a name="l00946"></a><span class="lineno">  946</span>&#160;</div>
<div class="line"><a name="l00947"></a><span class="lineno">  947</span>&#160;</div>
<div class="line"><a name="l00952"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_eigenvalue.html#ad01bfc213b887979f8f702acdd0a76c2">  952</a></span>&#160;   <span class="keywordtype">void</span> <a class="code" href="class_j_a_m_a_1_1_eigenvalue.html#ad01bfc213b887979f8f702acdd0a76c2">getV</a> (<a class="code" href="class_t_n_t_1_1_array2_d.html">TNT::Array2D&lt;Real&gt;</a> &amp;V_) {</div>
<div class="line"><a name="l00953"></a><span class="lineno">  953</span>&#160;      V_ = V;</div>
<div class="line"><a name="l00954"></a><span class="lineno">  954</span>&#160;      <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00955"></a><span class="lineno">  955</span>&#160;   }</div>
<div class="line"><a name="l00956"></a><span class="lineno">  956</span>&#160;</div>
<div class="line"><a name="l00961"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_eigenvalue.html#aae525e0f58b9ea03f183a4a75b46af50">  961</a></span>&#160;   <span class="keywordtype">void</span> <a class="code" href="class_j_a_m_a_1_1_eigenvalue.html#aae525e0f58b9ea03f183a4a75b46af50">getRealEigenvalues</a> (<a class="code" href="class_t_n_t_1_1_array1_d.html">TNT::Array1D&lt;Real&gt;</a> &amp;d_) {</div>
<div class="line"><a name="l00962"></a><span class="lineno">  962</span>&#160;      d_ = d;</div>
<div class="line"><a name="l00963"></a><span class="lineno">  963</span>&#160;      return ;</div>
<div class="line"><a name="l00964"></a><span class="lineno">  964</span>&#160;   }</div>
<div class="line"><a name="l00965"></a><span class="lineno">  965</span>&#160;</div>
<div class="line"><a name="l00971"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_eigenvalue.html#ad72ed4bd3a07325097a1ef4e36a0480f">  971</a></span>&#160;   <span class="keywordtype">void</span> <a class="code" href="class_j_a_m_a_1_1_eigenvalue.html#ad72ed4bd3a07325097a1ef4e36a0480f">getImagEigenvalues</a> (<a class="code" href="class_t_n_t_1_1_array1_d.html">TNT::Array1D&lt;Real&gt;</a> &amp;e_) {</div>
<div class="line"><a name="l00972"></a><span class="lineno">  972</span>&#160;      e_ = e;</div>
<div class="line"><a name="l00973"></a><span class="lineno">  973</span>&#160;      <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00974"></a><span class="lineno">  974</span>&#160;   }</div>
<div class="line"><a name="l00975"></a><span class="lineno">  975</span>&#160;</div>
<div class="line"><a name="l00976"></a><span class="lineno">  976</span>&#160;   </div>
<div class="line"><a name="l01010"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_eigenvalue.html#aee57a1213656385928a3fb2c6a21e4b2"> 1010</a></span>&#160;   <span class="keywordtype">void</span> <a class="code" href="class_j_a_m_a_1_1_eigenvalue.html#aee57a1213656385928a3fb2c6a21e4b2">getD</a> (<a class="code" href="class_t_n_t_1_1_array2_d.html">TNT::Array2D&lt;Real&gt;</a> &amp;D) {</div>
<div class="line"><a name="l01011"></a><span class="lineno"> 1011</span>&#160;      D = <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a>(n,n);</div>
<div class="line"><a name="l01012"></a><span class="lineno"> 1012</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l01013"></a><span class="lineno"> 1013</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a name="l01014"></a><span class="lineno"> 1014</span>&#160;            D[i][j] = 0.0;</div>
<div class="line"><a name="l01015"></a><span class="lineno"> 1015</span>&#160;         }</div>
<div class="line"><a name="l01016"></a><span class="lineno"> 1016</span>&#160;         D[i][i] = d[i];</div>
<div class="line"><a name="l01017"></a><span class="lineno"> 1017</span>&#160;         <span class="keywordflow">if</span> (e[i] &gt; 0) {</div>
<div class="line"><a name="l01018"></a><span class="lineno"> 1018</span>&#160;            D[i][i+1] = e[i];</div>
<div class="line"><a name="l01019"></a><span class="lineno"> 1019</span>&#160;         } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (e[i] &lt; 0) {</div>
<div class="line"><a name="l01020"></a><span class="lineno"> 1020</span>&#160;            D[i][i-1] = e[i];</div>
<div class="line"><a name="l01021"></a><span class="lineno"> 1021</span>&#160;         }</div>
<div class="line"><a name="l01022"></a><span class="lineno"> 1022</span>&#160;      }</div>
<div class="line"><a name="l01023"></a><span class="lineno"> 1023</span>&#160;   }</div>
<div class="line"><a name="l01024"></a><span class="lineno"> 1024</span>&#160;};</div>
<div class="line"><a name="l01025"></a><span class="lineno"> 1025</span>&#160;</div>
<div class="line"><a name="l01026"></a><span class="lineno"> 1026</span>&#160;} <span class="comment">//namespace JAMA</span></div>
<div class="line"><a name="l01027"></a><span class="lineno"> 1027</span>&#160;</div>
<div class="line"><a name="l01028"></a><span class="lineno"> 1028</span>&#160;</div>
<div class="line"><a name="l01029"></a><span class="lineno"> 1029</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01030"></a><span class="lineno"> 1030</span>&#160;<span class="preprocessor"></span><span class="comment">// JAMA_EIG_H</span></div>
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